Dzeko scored the second goal of the night as Roma picked up their first win of the season, with Bryan Cristante, Henrikh Mkhitaryan and Justin Kluivert also getting on the scoresheet before half-time.
But Sassuolo staged a mini-comeback in the second half, and Dzeko acknowledged that the side need to work on making sure that does not happen in future.
“I’m happy with the win but we should have done better in the second half,” Dzeko said.
“The main thing is to win, though, and make sure we keep improving.”
He added: “We relaxed a bit after going 4-0 up – even if the coach told us not to let up when he spoke to us during the break. I think it’s the same thing that happened this afternoon between Brescia and Bologna [Brescia led 3-1 at half-time, but lost 4-3]. It was similar for us but we struggled a bit in the second half.
“Physically there can be a bit of a drop with a game like this, given the heat and the fact a lot of us were away on international duty. But we’ll take this win and look ahead, hoping not to repeat again what happened in the second half. But, nevertheless, we played well.
“After going 4-0 up we lost the ball too much, perhaps because we were also trying to go forward too directly. But we have scored four goals, we could have even scored more, and we need to make sure we improve like that game-by-game.”
The game was perhaps most notable for Mkhitaryan’s debut goal, as the Armenian made a strong first impression in Italian football.
“Mkhitaryan is a great player, he’s played for a lot of top sides,” Dzeko said.
“Before the game I told him: you scored twice against Bosnia, now you need to help Roma win. His debut went well, but the more he settles in the better he will be.”
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